Energy and Power Engineering, 2013, 5, 661-666
doi:10.4236/epe.2013.54B128 Published Online July 2013 (
The Coupling of Voltage and Frequecncy Response in
Splitting Island and Its Effects on Load-shedding Relays*
Hao Yang, Baohui Zhang
School of Electrilcal Engineering, Xi’an Jiaotong University, Xi’an, China
Received February, 2013
The voltage and frequency dynamics interact with each other in the island after splitting. The current frequency re-
sponse model without considering the voltage effect would bring remarkable errors when analyzing the frequency dy-
namic progress in the island with large-capacity active-power shortage. In this paper, coupling effects of voltage and
frequency are studied to indicate that initial reactive-power deficit and load characteristics have strong effects on the
coupling effects of the voltage and frequency. Moreover, control effects of currently used under frequency load-shed-
ding relays (UFLS) and under voltage load-shedding relays (UVLS) which are installed and executed independently are
examined to find that it would sometimes cause excessive or inadequate control without considering the coupling, sug-
gesting that it is necessary to develop coordinate control methods for voltage and frequency problems.
Keywords: Frequency Response; Coupling Effects; Splitting Island; Coordination Control
1. Introduction
Frequency, voltage and angle stability are three main
kinds of power system stability, respectively [1]. How-
ever, when compared with the other two kinds, frequency
stability has drawn less attention [2]. Currently, power
grids in China has stepped into the age called large
power grids, high voltage and large units[3], the fre-
quency instability risk for the whole grid has decreased,
but the risk for the region grids has increased[4], espe-
cially with the growing amount of renewable energy.
Once the region grids disconnected with the main one
due to splitting accident, currently installed under fre-
quency load-shedding device (UFLS) may fail to ensure
the island frequency stability [5].
At present, the last line of defense ensuring frequency
stability is UFLS, whose setting is commonly based on
single-machine single-load frequency model, ignoring
voltage effects on frequency, such as the system fre-
quency response model (SFR) [6] and average system
frequency model (ASF) [7]. In fact, there are obvious
differences for voltage and frequency at different buses
due to space-time distribution characteristics [8]. How-
ever, there have been few studies about voltage effect on
frequency dynamic. Owing to load characteristics, the
negative effect of load-shedding on frequency recovery
was first reported in [9]. Considering load-voltage ef-
fectsless amount of load can be shed when UFLS per-
forms [10]. Although some researchers have realized the
value of coupling effects on frequency dynamic, the key
factors affecting the interaction and the mechanism have
not been analyzed carefully yet. Furthermore, few studies
have been done on the effect of the coupling on the third
line of defense for power system safety.
In this paper, we will analysis how the coupling affects
the frequency dynamic based on simulations of the con-
ventional system. Our results would help to find the key
factors affecting the interaction. Then the effects of the
coupling on the UVLS and UFLS performance are veri-
fied to indicate that it is necessary to develop the fre-
quency and voltage combined control method.
2. Frequency Changing Characteristic in the
The frequency response is decided by the active-power
balance dynamic on the generator as expressed in equa-
tions (1) - (4), which suggest that the load voltage can
affect the system frequency response through changing
the absorbed active-power of its own :
i mi etotal
eq ii
df PPP
dt 
 (1)
*The work Project Supported by State Grid Corporation of China,
Major Projects on Planning and Operation Control of Large Scale
Grid(SGCC-MPLG030-2 012)
,, ,
ie jlkl
 (2)
Copyright © 2013 SciRes. EPE
(, ,,)L.
PPUfxt j
(, ,)(M)
kk k
PgUUy k
 . (4)
where fcoi
Pi,m and Pi,e are the system inertia center fre-
quency, the mechanical and electromagnetic power of the
ith generator. Land M donates the load and line collec-
tions. P expresses active-power equation for loads, in
which x is the state variables. G expresses load loss equ-
The single-machine single-load frequency model im-
plies that the frequency can be predicted only by the in-
tial active-power shortage (ΔP0). This kind of model
agrees well with actual response data whenΔP0 is rela-
tively small. However, in some situations which may
cause large-capacity active-power shortage, for example
when the region grid is spitted from the main one, we
find the conclusions obtained from the conventional
model are quite different from the fact, sometimes even
opposite to the truth.
3. Simulation and Mechanism Analysis
3.1. Simulation Situations Description
The EPRI 36-bus system is as shown in Figure 1 in
which the governors and voltage regulator are carefully
considered, the load was modeled through a composite
model consisting of constant impedance and induction
motor considering rotor mechanical and electromagnetic
transient. All the eight generators adopt 6th –order model,
including governor and voltage regulator. Simulations
were conducted on power system analysis software
(PSASP) developed by China Electric Power Research
Institute (CEPRI), the integration step-size was 0.01 s,
total simulation time was 20 s.
A group of Lines (marked with X) was chosen as split-
ting section which divided the whole system into two
parts. Focus attention on the bottom right area with posi-
tive initial active-power deficit as shown in Figure 2.
Figure 1. EPRI 36-bus system.
To simplify the fault situation, the splitting accident
was simulated by disconnecting the section at 0.2 s.
Maintain the cross-section, effects of reactive-power
transferred through the cross-section and load character-
istics on the island frequency response were researched.
3.2. Effects of the Reactive-power Shortage
In conventional opinions, initial active-power shortage
(ΔP0) affects significantly the frequency response dy-
namic, but initial reactive-power shortage(ΔQ0) slightly
affects the frequency dynamic. However, after further
research we find the change of ΔQ0 has a remarkable
effect on the frequency response through voltage and
frequency coupling. Analyzing frequency without con-
sidering ΔQ0 would bring obvious errors.
Maintain ΔP0 at 6 p.u. (System base capacity is 100
MVA) , the change of ΔQ0 is as shown in Table 1.
Figure 3 shows the voltage curves observed at Node
Figure 2. The sketch map for isolated island after splitting.
Table 1. Initial reactive-power shortage chang conditions.
Power shortage conditions
Conditions Reactive-power
Percentage in load reac-
tive-power demand
1 0.5 8%
2 1 16%
3 1.25 20%
4 1.4 22.4%
5 1.5 24%
6 1.6 25.6%
7 2 32%
8 2.5 40%
Copyright © 2013 SciRes. EPE
H. YANG, B. H. ZHANG 663
It can be seen from Figure 3 that the voltage decreases
as ΔQ0 increases, which can also be observed at other
buses. From Equations (3) it can be noted that island
voltage affects the total active-power absorbed by loads
(PL). From Equations (2) it can be seen that PL is the
major part of the total electromagnetic active-power of
the island(Pe). Figure 4 shows the change of Pe with
different ΔQ0:
From Figure 4 it can be observed that Pe decreases
with ΔQ0 increases. When the ΔQ0 increases over a cer-
tain threshold, Pe drops sharply due to the voltage de-
Meanwhile the change of total mechanical power in
the island (Pm) decided by governors at generators is as
shown in Figure 5:
Figure 3. Voltage of Bus 16 under different ΔQ0.
Figure 4. Values of total Pe under different ΔQ0.
Figure 5. Total Pm under different ΔQ0.
The difference between Pm shown in Figure 5 and
Pe shown in Figure 4 ,which is called unbalanced ac-
tive-power (ΔPtotal) is shown in Figure 6.
From Equations (1) it can be seen that ΔPtotal decides
the frequency dynamic of the island, which is shown in
Figure 7.
It can be seen from Figure 7 that:
1) Under all conditions, frequency drops at the initial
moment, the dropping rate of frequency decreases when
ΔQ0 increases, but the differences among all of the con-
ditions are slight.
2) Effects of change of ΔQ0 on frequency appears ap-
parently after 0.4 s. When ΔQ0 increases(See Figure 3) ,
voltage decreases ,leading to the decrease of PL due to
voltage effects on the load active-power. Then Pe de-
creases (See Figure 4), causing the increase of ΔPtotal
(See Figure 6). As a result, the frequency decided by
ΔPtotal increases when ΔQ0 increases. If ΔQ0 exceeds a
certain threshold(e.g., 2 p.u.), causing voltage instability
at some load buses, leading sharp drop of PL, whose
decline value can be higher thanΔP0, causing the sign of
ΔPtotal to change ,and then the frequency of the island
would exceed rating value(i.e., 50 Hz) despite of the se-
vere ΔP0.
From above discussions it can be implied that the fre-
quency changing trend cannot be predicted accurately
only byΔP0. ΔQ0 affects the voltage, changing frequency
dynamic. Conclusions without considering ΔQ0 can be
far from, sometimes even inverse to the truth. It is nec-
essary to consider reactive-power balance when analyz-
ing island frequency.
Figure 6. Unbalanced active-power under different ΔQ0.
Figure 7. Frequency response under different ΔQ0.
Copyright © 2013 SciRes. EPE
3.3. Effects of Load Characteristics
Maintain power transferred through the cross-section at
6+j1.5. The load characteristic was varied by changing
the percentage of induction motor in the compositive
load as shown in Table 2.
Figure 8 shows voltage of Bus 16:
It can be seen that the percentage of induction motor
has a remarkable effect on voltage response. When the
percentage increases, voltage decreases .When the per-
centage exceeds 30%, the motor instability happens due
to voltage drop, whose active-power decreases sharply as
well as the reactive-power clearly increases .The change
of motor variables when the percentage is 40% is as
shown in Figure 9.
In Figure 9, V,s,P and Q represent slip ratio, voltage,
active-power, reactive-power of the motor, respectively.
The change of Pe is as shown in Figure 10:
It can be seen From Figure 10 that Pe decreases with
the percentage increases.
The frequency change curves in various situations are
as shown in Figure 11:
ΔPtotal is as shown in Figure 12:
It can be seen that the percentage of induction motor
significantly affects the frequency dynamic through
changing the island voltage. ΔPtotal and frequency in-
crease with the percentage increses. While the percentage
exceeds a certain threshold, the sign of ΔPtotal would
change, causing that frequency of the island exceeds rat-
ing value despite of severe ΔP0.
Table 2. Loda characteristic change in the island.
Load model component
Model Induction motor(%) Constant impedance(%)
1 0 100
2 20 80
3 25 75
4 30 70
5 35 65
6 40 60
7 45 55
Figure 8. Voltage of Bus16 under different load characteristics.
Figure 9. Related variables of the motor at Node 16 under
different load characteristics.
Figure 10. Response curves of total Pe in the isolated island
under different load characteristics.
Figure 11. Response curves of frequency in the isolated is-
land under different load characteristics.
Figure 12. Comparisons of unbalanced active-power in the
isolated island under different load characteristics./
Copyright © 2013 SciRes. EPE
H. YANG, B. H. ZHANG 665
4. Effects of the Coupling on Load –shedding
4.1. Load-shedding Devices Installed Situations
and Existing Problems
In current China’s power grids underfrequency load-
shedding (UFLS) and undervoltage load-shedding
(UVLS) are two different kinds of devices installed to
prevent frequency and voltage instability, respectively.
However, these two kinds of devices are set and perform
independently despite of the coupling between frequency
and voltage .Lacking the coordination between them
would result in excessive or insufficient control.
The UFLS and UVLS installations adopted in current
Shanxi Province in China are as shown in Table 3 and
Table 4.
The load-shedding devices are both installed at each
load node of the island.
We research control effects of the current load-shed-
ding device on the island with the coupling of voltage
and frequency.
4.2. Control Effects When ΔQ0 Changes
Table 5 shows the control effects with different ΔQ0, the
conditions are just the same as shown in Table 1.
From Table 5 it can be seen that:
1) The total shedding amount carried out by UVLS
and UFLS decrease as ΔQ0 increases.
2) The shedding amount carried out by UVLS in-
creases as ΔQ0, UVLS cannot start When ΔQ0 is less
than a certain threshold.
3) The shedding amount carried out by UFLS in-
creases as ΔQ0 decreases, UFLS cannot start When ΔQ0
is more than a certain threshold.
Table 3. UFLS setup situations.
Setup stages
fset(Hz) 49 48.8 48.6 48.4 48.2 48 49
Tdelay(s) 0.2 0.2 0.2 0.2 0.2 0.210
Pshed(%) 7 7 7 7 7 7 4
Table 4. UVLS setup situations.
Setup turns
Uset(p.u.) 0.85 0.8 0.75 0.85
Tdelay(s) 1 1 1 10
Pshed(%) 7 7 7 4
4) Lack of coordination between UVLS and UFLS
would cause excessive control ( i.e, fmax > 51 Hz) under
some conditions(e.g.,ΔQ0=1,1.5), in which low fre-
quency and low voltage happen at the same time.
5)Currently used load-shedding relays may not prevent
island from collapse under some situations(e.g. ΔQ0 =
2,2.5),in which high frequency and low voltage happen at
the same time, causing that UFLS cannot act and UVLS
is too late to shed insufficient amount of load.
4.3. Control Effects When Load Characteristics
Table 6 shows the control effects, the conditions are just
the same as shown in Table 2 .
What can be seen From Table 6 are similar to those
obtained from Table 5 :
1) The total shedding amount decreases as the per-
centage of induction motor in load increases.
2) The shedding amount carried out by UVLS in-
creases as the percentage, UVLS cannot start when the
percentage is less than a certain threshold.
3) The shedding amount carried out by UFLS in-
creases as the percentage decreases, UFLS cannot start
when the percentage is more than a certain threshold.
4) Lack of coordinates between UVLS and UFLS
would cause excessive control (i.e, fmax> 51Hz) under
some situations (e.g., the percentage equals 30%), in
Table 5. Control effects when ΔQ0 changes.
Control Effects
Codition 0
(Hz) Umin (p.u)
1 0.5I-IV(4.69)\ 50.89 48.10 0.998
2 1 I-IV(4.69)I ( 0.76 ) 51.21 48.30 0.999
3 1.5I-III(3.52)I,II(1.16) 51.16 48.33 0.943
4 1.6I,II(2.35)I,II(1.88) 50.67 48.55 0.925
5 2 \ I-IV(3.96) 51.59 49.83 0.649
6 2.5\ I-IV(3.99) 52.34 49.94 0.576
For example, I-IV(4.69) means that UFLS performs four steps with 4.69 p.u.
load shed.
Table 6. Control effects with different load characteristic.
Control Effects
Codition Motor
1 20 I-III(3.52)I(0.76) 50.85 49.760.933
2 25 I-III(3.52)I(0.76) 50.83 48.750.931
3 30 I-III(3.52)I,II(1.16) 51.11 49.990.967
4 35 \ I-IV(3.60) 51.56 50.660.628
5 40 \ I-IV(3.99) 52.35 51.170.606
Copyright © 2013 SciRes. EPE
Copyright © 2013 SciRes. EPE
which low frequency and low voltage happen at the same
5)The present UVLS and UFLS may not prevent is-
land from collapse under some situations(e.g., the per-
centage equals 35% or 40% ),in which high frequency
and low voltage happens at the same time, causing that
UFLS cannot act and UVLS is too late to shed insuffi-
cient amount of load.
5. Conclusions
The island frequency response is decided by both me-
chanical power and electromagnetic power. Island volt-
age affects electromagnetic power, which change the
frequency dynamic in island. Initial reactive-power defi-
cit and load characteristics are two key factors affecting
the frequency response dynamic through coupling of
voltage and frequency when initial active-power main-
tains unchanged.
When initial reactive-power or percentage of induction
motor in loads increases, the voltage decreases, leading
the decrease of total electromagnetic power. As the de-
crease of unbalanced active-power in island, the decrease
of frequency decline rate and the increase of frequency.
While initial reactive-power deficit or percentage of in-
duction motor in load exceeds a certain threshold, the
signal of unbalanced active-power in island would
change, which may cause high frequency despite of se-
vere active-power deficit in the island.
Ignoring the coupling of voltage and frequency dy-
namic would result in remarkable errors when analyzing
the frequency response of the splitting island with large
initial active-power deficit.
Moreover, the currently used UVLS and UFLS, whose
setup and performance are independent without consid-
ering the coupling of voltage and frequency, would cause
excessive when low voltage and low frequency happen at
the same time or insufficient control when initial reac-
tive-power deficit or percentage of induction motor in
load exceeds a certain threshold.
It is necessary to develop coordination control for vol-
tage and frequency on the basis of research on their cou-
pling effects.
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